Problem: Simplify the following expression: $\dfrac{4q^4}{16q^5}$ You can assume $q \neq 0$.
Answer: $ \dfrac{4q^4}{16q^5} = \dfrac{4}{16} \cdot \dfrac{q^4}{q^5} $ To simplify $\frac{4}{16}$ , find the greatest common factor (GCD) of $4$ and $16$ $4 = 2 \cdot 2$ $16 = 2 \cdot 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(4, 16) = 2 \cdot 2 = 4 $ $ \dfrac{4}{16} \cdot \dfrac{q^4}{q^5} = \dfrac{4 \cdot 1}{4 \cdot 4} \cdot \dfrac{q^4}{q^5} $ $\phantom{ \dfrac{4}{16} \cdot \dfrac{4}{5}} = \dfrac{1}{4} \cdot \dfrac{q^4}{q^5} $ $ \dfrac{q^4}{q^5} = \dfrac{q \cdot q \cdot q \cdot q}{q \cdot q \cdot q \cdot q \cdot q} = \dfrac{1}{q} $ $ \dfrac{1}{4} \cdot \dfrac{1}{q} = \dfrac{1}{4q} $